TY - JOUR
T1 - Compact Kähler manifolds with nonpositive bisectional curvature
AU - Liu, Gang
N1 - Publisher Copyright:
© 2014, Springer Basel.
PY - 2014/9/1
Y1 - 2014/9/1
N2 - Let (Mn, g) be a compact Kähler manifold with nonpositive bisectional curvature. We show that a finite cover is biholomorphic and isometric to a flat torus bundle over a compact Kähler manifold Nk with c1 < 0. This confirms a conjecture of Yau. As a corollary, for any compact Kähler manifold with nonpositive bisectional curvature, the Kodaira dimension is equal to the maximal rank of the Ricci tensor. We also prove a global splitting result under the assumption of certain immersed complex submanifolds.
AB - Let (Mn, g) be a compact Kähler manifold with nonpositive bisectional curvature. We show that a finite cover is biholomorphic and isometric to a flat torus bundle over a compact Kähler manifold Nk with c1 < 0. This confirms a conjecture of Yau. As a corollary, for any compact Kähler manifold with nonpositive bisectional curvature, the Kodaira dimension is equal to the maximal rank of the Ricci tensor. We also prove a global splitting result under the assumption of certain immersed complex submanifolds.
UR - https://www.scopus.com/pages/publications/84907701064
U2 - 10.1007/s00039-014-0290-7
DO - 10.1007/s00039-014-0290-7
M3 - 文章
AN - SCOPUS:84907701064
SN - 1016-443X
VL - 24
SP - 1591
EP - 1607
JO - Geometric and Functional Analysis
JF - Geometric and Functional Analysis
IS - 5
ER -